Skid control apparatus

ABSTRACT

In the skid control apparatus disclosed a wheel velocity detector detects the velocity of a wheel on a vehicle that is being slowed down by application of a brake. A braking pressure detector detects the pressure created in a brake fluid in a brake line passing from a master cylinder to a brake cylinder. A control circuit establishes a predetermined or set wheel velocity from the vehicle&#39;&#39;s deceleration, the vehicle velocity, the rate at which the braking fluid pressure is increased, the gradient of the characteristic curve representing the relationship between the coefficient of friction of the road surface on which the vehicle travels and the wheel slip ratio. The control circuit then compares the set wheel velocity and the actually measured wheel velocity. When the actual wheel velocity is lower than the set wheel velocity, thereby indicating that the deceleration of the wheel has been more rapid than the set or desired deceleration, the control circuit issues a signal indicating excessive deceleration. A pressure regulator responds to this signal by decreasing the pressure of the braking fluid in accordance with this signal of the control circuit.

United States Patent [1 1 Ochiai SKID CONTROL APPARATUS Takeshi Ochiai,Toyota-shi, Aichi-ken, Japan Inventor:

[73] Assignee: Toyota Jidosha Kogyo Kabushiki Kaisha, Aichi-ken, JapanFiled: July 21, 1971 Appl. No.: 164,672

[30] Foreign Application Priority Data Oct. 2, 1973 57 ABSTRACT In theskid control apparatus disclosed a wheel velocity detector detects thevelocity of a wheel on a vehicle that is being slowed down byapplication of a brake. A braking pressure detector detects the pressurecreated in a brake fluid in a brake line passing from a master cylinderto a brake cylinder. A control circuit establishes a predetermined orset wheel velocity from the vehicles deceleration, the vehicle velocity,the rate at which the braking fluid pressure is increased, the gradientof the characteristic curve representing the relationship between thecoefficient of friction of the road surface on which the vehicle travelsand the wheel slip ratio. The control circuit then compares the setwheel velocity and the actually measured wheel velocity.

[56] References Cited When the actual wheel velocity is lower than theset UNITED STATES PATENTS wheel velocity, thereby indicating that thedeceleration 3,131,975 5/1964 Smith et al. 303/21 P of the Wheel hasbeen more rapid than the Set or 3,362,757 1/1968 Marcheron 303/21 Psired deceleration, the control circuit issues a signal in- ,6 7 9 dan303/21 BE dicating excessive deceleration. A pressure regulator3,622,208 11/1971 g 188/131 C X responds to this signal by decreasingthe pressure of the 3,650,575 3/1972 Okamoto 188/181 C X braking fl idin accordance with this Signal f the trol circuit.

29 Claims, 13 Drawing Figures 7\ i 8| 82 e9 1 w 5 VELOCITY w I SUBTRAC--f COMPARA- DET MEMORY TOR a TOR 5 'di 1 i so INTEGRA- TOR AMPL was? l IDET y 9 60 P AMPL ADDER AccELERoMErEFUT'i: I 1 8 KZPV I WHEEL? 8 Kmnepvi TORQUE 5 9 DETECTOR P I as a? Piur'Pv MgRDULA- West ER I g T lDIFFEREN. P MULTIPLIER l s l t l l .1 5t

WHEEL CYL SKID CONTROL APPARATUS REFERENCES TO COPENDING APPLICATIONSThis application is related to the following copending applications. Thedisclosures in all of these applications are hereby made a part of thisapplication as if fully recited herein:

Applications of Takeshi Ochiai, Ser. No. 109,461 filed Jan. 25, 1971,entitled SKID CONTROL SYS- TEM FOR VEHICLES, and Ser. No. 109,465 filedJan. 25, 1971 entitled SKID CONTROL SYSTEM, both now abandoned in favorof Continuation-in-Part Applications Ser. No. 270,584, entitledSKIDCONTROL SYSTEM FOR VEHICLES, and all assigned to the same assignee asthis application;

Application of I-Iiroshi Arai et al., Ser. No. 137,858, filed Apr. 27,1971, entitled VEHICLE BRAKESYS- TEMS USING SKID CONTROL DEVICES, andassigned to the same assignee as this application, now abandoned andpending as Divisional Application Ser. No. 162, 405 filed Jan. 5, 1973,filed July 14, 1971.

BACKGROUND OF THE INVENTION This invention relates to skid controlsystems for preventing the wheels of a vehicle from locking and.skidding in response to excessive brake pressure, and particularly tosuch systems incorporating devices for establishing a predetermineddesired deceleration. The invention relates more generally to vehiclebrake systems, vehicles themselves, and methods for skid control in suchbrake systems.

Such skid control systems may be used, for example, with automobiles. Insuch systems a pressure regulator reduces or relieves the pressureapplied by the vehicles master cylinder when a controller detects thefact that the wheel velocity, as measured by a wheel sensor isdecreasing faster than a safe deceleration. Several embodiments of suchsystems are disclosed in the beforementioned copending applications.

In general suchsystems attempt to bring a vehicle to a halt within aminimum braking distance without causing loss of control or spinning ofthe vehicle body due to wheel lock. The attempt is to regulate thepressure to the brake on the wheel to produce the above effectsregardless of the physical effort applied to the brake pedal when anoperator attempts to stop the vehicle, such as in an emergency.

Such skid control systems rely upon a factor known as the wheel slipratio, namely the fractional departure of the wheel velocity from thevehicle velocity. Recognizing that the maximum coefficient of frictionbetween a wheel and a road surface during braking occurs when the wheelslip ratio is in the range of from 0.l5 to 0.2, such skid controlsystems regulate the wheel slip ratio so as to remain at a constantvalue by pickingan arbitrary value within that rangeof wheel slip ratiosand setting it. Consequently, skid control produced ac,- cording to suchsystems relies upon this constant value. Therefore, optimum skid controlcannot be obtained if the wheel slip ratio at which the coefficient offriction. is maximum changes due to changes in the character of the roadsurface, vehicle velocity, shape of the tire, or other factors. Thus,such skid control devices leave much to be desired.

An object of this invention is to improve skid control systems andmethods.

Another object of this invention is to obviate the disadvantages offormer skid control systems.

Still another object of this invention is to bring vehicles to haltwhile the coefficient of friction between the road surface and the wheelis at a maximum, regardless of whether the road surface, vehiclevelocity or other factors are changed. Still another object of theinvention is to insure optimum skid control where a wheel is likely tolock.

SUMMARY OFWTHE INVENTION According to a feature of the invention theseobjects .are obtained in a skid control apparatus wherein regulatormeans relieve the braking force applied by a brake applicator to a wheelbrake by establishing a set deceleration. The set deceleration isestablished by the sum of one value corresponding to the brake pressureand a second value proportional to the product of the initialcoefficient-of-friction wheel-slip-ratio curve and the differentialvalue of the brake pressure as well as the vehicle velocity. Controlmeans cause the regulator means to relieve the braking force supplied bya brake applicator to a wheel brake when the control means de-' tectsthat the wheel velocity declines at a rate exceeding the setdeceleration.

According to another feature of the invention a comparator determineswhether the wheel velocity declines at a rate exceeding the safe setrate by comparing the instantaneous wheel velocity with the wheelvelocity that existed when braking was initiated diminished by a timeintegral of the set deceleration over the time since braking had beeninitiated. This compares the instantaneous wheel velocity with thevelocity that would exist had the set deceleration been prevelant sinceinitiation of braking. If the instantaneous velocity is lower, therebyindicating excessive deceleration, a pressure relieving signal isapplied to the regulator.

According to a more general feature of the invention a continuouslychanging set velocity subsequent to the initiation of braking isestablished. The instantaneous velocity is then compared with the setvelocity.

According to another feature of the invention the velocity at initiationof braking is established as an electrical value which is diminished bya constant current corresponding to the brake pressure and a decliningcurrent.

These and other features of the invention are pointed out in the claims.Other objects and advantages of the invention will become obvious fromthe following detailed description when read in light of theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic drawingillustrating a brake arrangement with a skid control apparatus eachembodying features of the invention;

FIG. 2 is a graph illustrating various characteristics of coefficientsof friction for wheel slip ratios in vehicles, such as those in FIG. 1.

FIG. 3 is a schematic drawing of the wheel in FIG. 1 showing variouscharacteristics of the wheel and its brake;

FIG. 4 is a graph illustrating changes in the pressure applied to thewheel cylinder of the wheel in FIG. 1 by operation of the brake pedal inFIG. 1 over a specified time period;

FIG. is a graph illustrating changes in coefficients of friction forvarious wheel slip ratios under different conditions;

FIG. 6 is a block diagram of a system forming a portion of FIG. 1 andembodying features of the invention;

FIG. 7 is a partially schematic, partially block circuit diagram ofanother embodiment of portions of the system forming a part of FIG. 1;

FIG. 8 is a partially schematic partially block diagram of a controlcircuit forming a part of. FIG. 1 and embodying features of theinvention;

FIG. 9 is a schematic diagram of another embodiment of the controlcircuit of FIG. 1;

FIG. is a hydraulic circuit diagram illustrating an embodiment of theregulator shown in FIG. 1;

FIG. 1 la is a graph illustrating variations with respect to time ofvoltages proportional to the actual wheel velocity and the set wheelvelocity for various conditions in FIGS. 1, 9 and 10;

FIG. 1 1b is a graph illustrating the deceleration of the wheel in FIG.I for the variation illustrated in FIG. 11a; and

FIG. 110 is a graph illustrating the variation in fluid pressures at thewheel cylinder of FIG. 1 for the condition shown in FIGS. 11a and 11b.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS The following descriptionis made with respect to an automobile brake system, but may beapplicable to brake systems of other vehicles and is not limited to theautomobile.

In FIG. 1 a brake pedal 1 of automobile A embodying features of theinvention actuates a master cylinder 2. The brake pedal 1 and the mastercylinder 2 serve to control rotation of a wheel 3 forming part of theautomobile by means of a brake shoe 4 and a wheel cylinder 5. The latterreceives brake fluid under pressure from the master cylinder 2 through abrake line or hydraulic pressure line BL. A pressure detector 6 on thehydraulic pressure lineand forming part of the automobile A detects thebrake pressure in the wheel cylinder 5. A

velocity detector or generator 7 detects the rotational speed of thewheel in the vicinity of the wheel 3. A control circuit responds to theelectrical signals from the detector 7. The control circuit 8 alsoforming part of the automobile A and this invention elecricallyregulates a pressure regulator 9 through electrical lines 10 and 11. Thepressure regulator 9 intervenes between the master cylinder 2 and thewheel cylinder 50 so as to control the pressure in the wheel cylinderand set it at an optimum value.

Under normal travel conditions, when the skid control system forming apart of the brake system is not required to operate, the pressure ofbrake fluid supplied to the master cylinder 2 conforms to the amount ofphysical effort applied to the brake pedal 1. This pressure is appliedwithout change to the wheel cylinder 5 so as to produce a correspondingbraking force. This decelerates the rotational speed of the wheel 3. The

pressure detector 6 senses this braking pressure being applied to thewheel cylinder 5.

When emergency braking is applied on the pedal 1 there is danger thatthe wheel 3 may lock due to depletion of the frictional force betweenthe wheel and the road surface. If such a danger exists the controlcircuit 8 then responds to the wheel velocity detected by the wheelvelocity detector 7 to issue a pressure reduction signal. By means ofthe latter the pressure regulator 9 shuts off or reduces the flow ofbrake fluid from the master cylinder 2. It then regulates the pressureof the fluid in the wheel cylinder 5. By preventing the wheels fromlocking in this manner, the vehicle is brought to a halt within aminimum stopping distance.

In FIG. 2 changes in various coefficients of friction y. of wheels, suchas the wheel 3, are plotted along the ordinate of the rectangularcoordinates, while the wheel slip ratio a is plotted along the abscissa.The wheel slip ratio is defined as the fractional change in wheelvelocity as compared to the vehicle velocity, namely (v-w)/v, where vrepresents the vehicle velocity and w the wheel velocity. Thus FIG. 2illustrates 4,-0- curves that vary in ways depending upon road surfaceconditions or vehicle speed or both. Generally it has been determinedthat the part of curves between the point where the wheel slip ratio 0'is zero and the point where the u-a curve is curved, that is in thevicinity of the point where p. is maximum, or the knee of the curve,proceed along a straight line having a constant gradient drr/dp. at anangle 0 as shown in curves A, B and C. There are some variationdepending on the conditions of the road surfaces. A curve such as thecurve D is someiimes detected. Nevertheless generally the curves proceedin a straight line from zero to the knee of the curves. along theconstant gradient do-ldu. Al-

though the variations exist it can safely be assumed that the gradientof all these curves is substantially constant.

FIG. 3 illustrates schematically a number of dimensions for analyzingthe opeation of the wheel 3 as it and the vehicle travel and brakes areapplied. FIG. 2 illustrates the vehicle velocity v, the wheel velocityw, and

the force BP=F between the brake shoe and the drum.

The value P represents the pressure between the brake shoe and the drumor the pressure of the brake fluid, the latter being proportional to theformer, while B is a constant which may, for example, represent the areaof contact between the brake shoe and the drum.

FIG. 3 also illustrates the effective radius R of the wheel 3, theradius r of the brake drum, the coefficient of friction 11. between thebrake shoe and the drum, the coefficient of friction between the roadsurface and the wheel pi, and the braking torque T.

In discussing these dimensions reference will be made to thedeceleration G of the wheel 3, the gradient 0/ =tan 0 of the [.L-O'curve, the moment of inertia I of the wheel, the time t, and thegravitational acceleration FIG. 4 illustrates the relationship betweenthe pressure P of the brake fluid in the wheel cylinder 5 at differenttimes 1. FIG. 5 shows the u-o' curves under two different roadconditions which are respectively represented by the curves A and B.

The relationships between these various factors are duscussed withreference to FIGS. 1 and 6 wherein the latter illustrates an emboidmentof the control circuit 8 and its connections to the pressure regulator 9and the velocity detector 7 as well as the pressure detector 6. In FIGS.1 and 6 the pressure detector 6 responds to the hydraulic pressure inthe wheel cylinder 5 by generating a signal P corresponding to thepressure in the brake line or wheel cylinder. At the same time the wheelvelocity detector 7 furnishes a signal corresponding to the wheelvelocity w. Both the signals at the output of the pressure detector 6and the wheel velocity detector 7 are passed to the control circuit 8 toperform its skid controlling function. Thus the control signal from thecontrol circuit 8 is transmitted to the pressure modulator 9.

In FIG. 6 the output signal of w of the wheel velocity detector 7 passesto an initial velocity memory circuit 81 as well as a comparator 89. Theinitial velocity memory circuit 81 memorizes the wheel velocity w at thetime when braking is started. It thus maintains this velocity as itsoutput. In general the memory circuit detects the sudden decrease inwheel velocity that occurs when the brakes are applied and memorizesthis value. On the other hand the hydraulic pressure P in the wheelcylinder 5 which is detected by the pressure detector 6 is passed to alinear amplifier 85. The latter produces a signal a whose value is equalto K P or gKP. The values K, and K are constants which include theconstant A differentiator 86 differentiates the pressure P to obtain theso-called pressure speed P or the rate of change of pressure. Amultiplier 87 produces the product of the pressure speed and the vehiclevelocity v. According to this embodiment of the invention the vehiclevelocity v is determined for slip ratios less than 0.2. Under thesecircumstances the set wheel velocity w,, which is produced within thecircuit 8 and which represents the desired safe wheel velocity at anytime, equals v. The output of the multiplier 87 is thus equal to P'w,=P'v.

A linear amplifier 88 multiplies the value at the output of themultiplier 87 to a value K P'v. Here again the constant K includes theconstant [3 which represents the proportion between the pressure P andthe force F between the brake shoe and the drum. The output of theamplifier 88 thus produces a signal 6 equal to K P'v=Ktan0 P'v, where Kis a constant including the value. An adder 84 adds the values of thesignal a and e which together equal gKP+K tangent tanOP'v. This sumrepresents the set wheel deceleration w which corresponds to the desiredsafe deceleration. An integrator 83 integrates the deceleration w withrespect to time. A subtractor 82 then subtracts the value fw'dt from theinitial velocity w memorized by the memory circuit 81. The result, w, w,fw'dt represents the set wheel velocity w, which represents the velocitythat a wheel should exhibit at any time so as to be decelerated withoutlocking within the range of a slip ratio smaller than that at which thecoefficient or friction is maximum.

The comparator 89 compares the set wheel velocity w, with theinstantaneous wheel velocity w to derive a pressure reducing signal whenthe actual wheel velocity w is lower than the set wheel velocity w,.This signal is amplified by an amplifier 90 and serves to actuate thepressure regulator 9 to decrease the hydraulic pressure in the wheelcylinder 5. In other words, when the wheel is decelerated at a speedhigher than the theoretical deceleration; that is when the slip ratioexceeds the maximum coefficient of friction and the wheel is about tolock the comparator 89 produces an output signal. Generally the pressuremodulator 9 is actuated by means of an electromagnetic valve with alight. Where the velocity w is greater than the set wheel velocity w,

the comparator 89 produces no output. The regulator 9 thus allows themaster cylinder 2 to apply full brake pressure to the wheel cylinder 5.No decrease in the pressure is produced. In other words, where the wheelis deceleraed at a rate lower than the theoretical safe deceleration nochange in deceleration is necessary.

The control circuit 8 thus calculates the deceleration w to be developedwhen the wheel 3 is decelerated in the range of slip ratios from zero tothe slip ratio at which the coefficient of friction is maximum. On thebasis of the wheel velocity w when braking is initiated and thedeceleration w, the control circuit 8 also calculates the set wheeldeceleration w,="W fw'dt. This set wheel deceleration is theintantaneous deceleration at which the wheel 3 is safely deceleratedwithout locking and with a slip ratio less than at which the coefficient of friction p. is at a maximum. The control circuit 8 thencompares the set wheel velocity w, and the actual wheel velocity w atthat moment and applies a signal for decreasing the hydraulic pressurein the wheel cylinder 5 to the pressure modulator 9 when the actualvelocity w is smaller than the set wheel velocity w,. That the controlcircuit 8 as illustrated in FIG. 6 actually produces signals only whenthe deceleration exceeds the optimum deceleration regardless of variousroad conditions can be demonstrated from the ordinary equations ofmotion of a wheel at the time the brakes are applied. These equationsutilize the beforementioned symbols illustrated in FIGS. 2 through 5. Ingeneral the symbols represent the following:

v vehicle velocity w wheel velocity P pressure of the braking fluid F orflP force between brake shoe and the drum of FIGS. 3 and 5. R effectiveradius of the wheel 3 r radius of the brake drum 4 n coefficient offriction between brake shoe and drum. p. coefficient of friction betweenthe road surface and wheel 3. T the braking torque G wheel decelerationtanO Aa/Ap. the gradient of the u-o curve I moment of inertia of thewheel 3 t time 3 gravitational acceleration Of the following equationsthe first expresses the relation that the moment of inertia of the wheelmultiplied by its rotational acceleration is equal to the net torque.The second equation expresses the relation that acceleration is equal tominus deceleration. The third equation defines the wheel slip ratio. Thefourth equation defines tan0 at the knee of the curves in FIG. 1. Thefifth equation defines the torque imposed by the braking force on thewheel.

1 (dw/dt) R a W z pp v HO) tan 0 cr/u (wherein, A 0 a T rpL BP Inequation 4, 0,, represents the wheel slip ratio where the u-o' graphstarts to curve as is shown in FIG. 2.

We can assume that the pressure P, of a brake fluid being applied at thetime P, increases linearly to P; at the time t, after an elapse of timeAt as shown in FIG. 4. We also assume that the vehicle velocitysimultaneously decreases and the wheel slip ratio 0 changes from 0-, to0- as illustrated in FIG. 5. If we substitute these conditions inequation number of 3 then second term in the parentheses of equation 9because it is far smaller than the first term. Thus az tan6 (ZFP-o/R W)BP Substituting the equation 10 into equation 8 we obtain the value Ifthe behavior of a wheel is considered over a short period of time, thedeceleration dw/dt of the wheel is expressed as follows:

dw/dt 135 O/( Thus dw/dr lim [(l [0 031/2)", v, lAt) tan&

( M/ (3 B r/ ID] In the above equations '1 I L l s/ '1 Thus dw/dt g (l0' (dv ldt) tan!) (ZU /RW) (Bdp/dt) The foregoing makes it apparent thatthe acceleration of the wheel caused when the brake pressure P having apressure change dP/dt is applied to the wheel having a velocity v attime 1 is expressed by equation 13. This change occurs regardless of thecoefficient of friction between the wheel and ground.

The coefficient of friction s is determined by modifying equation I.

As mentioned before, the term including the moment of inertia of thewheel is assumed to be far smaller than the term concerning the brakingfrictional force. Therefore, omitting the first term of equation 1' Ifequation 1"is substituted in equation 2 as well as in equation 5 It isthus apparent that the vehicle acceleration is proportional to thepressure or braking torque.

The calculations described thus far derive the wheel acceleration. Toexamine the phenomena occuring during brake application it is necessaryto consider the wheel deceleration. If wheel deceleration is defined asw with its attendant vehicle deceleration and pressure reducing changerepresented by v and P respectively then the relationship between themis as follows:

In the range where the gradient of the p.o' curve is mm) and constant,the value of a in equation 13 is generally small and Assuming that l 0'l, i

equation 13 may be rewritten as follows:

w v' KtanO P'v,

(IS-l) Where K is constant and equals 2ru B/RW From the above it isevident that the wheel deceleration occurring during optimum brakingconditions equals the sum of a term proportional to the vehicledeceleration v and a term obtained by multiplying the gradient tan ofthe u-o curve by the rate of pressure change of the brake fluid and thevehicle velocity v. In effect this shows that optimum skid controldepends upon the rate of pressure change, the so-called pressure speed,and the vehicle velocity. From equation 14 it can be seen that thevehicle deceleration is related to the brake pressure and the brakingtorque. Therefore the equation 15-1 may be rewritten as follows:

-g (2/RW) 7'+ (Klru tanHTv As can be seen, the output of the adder 84produces a value w equal to the value in equation 15-2.

As shown in FIG. 6 the control of wheel deceleration is performed on thebasis of equation 15-2 as described above. This produces the signal w'corresponding to the vehicle deceleration and the signal correspondingto the product of the gradient tanO of the u-o' curve, braking pressurespeed P and vehicle velocity. The vehicle deceleration may also beexpressed in terms of brake pressure and braking torque. The rate ofchange of pressure, or pressure speed, P may be expressed as a functionof the rate of change of torque T or. torque speed.

The set deceleration of a wheel expressed by the sum of both of thesesignals is established by the adder 84. Skid control is performed bysubtracting the integral of the set deceleration from a wheel speed atthe start of the braking action. This subtracted value is then comparedwith the instantaneous wheel speed.

According to another embodiment of the invention the decelerationdetector 6 in FIG. 6 is composed of an accelerometer 6a and a wheeltorque or pressure detector 6b. That such a substitution is possible canbe seen by considering equation 15-1, 15-2 and 15-3 together. Evidentlythe first term in equation 15-2 represents the vehicle deceleration. Thesecond term can then be passed to the differentiator 86 either in theform of pressure P or braking torque T as indicated by equation I5-2 or-3.

According to another embodiment of the invention the vehicledeceleration detector or decelerometer is in the form of means adaptedto detect the braking pressure or braking torque. Thus, provision of anaccelerometer is not required since the braking pressure and brakingtorque correspond to the vehicle deceleration. The rotational speed ofthe wheel, i.e. the wheel velociry w is always detected by means of thewheel velocity detector 7. Both output signals of the pressure detector6 and the wheel velocity detector 7 are passed to the control circuit 8so the latter performs the skid control and passes a skid control signalto the pressure modulator or regulator 9.

In the control circuit 8 of FIG. 6 the signal at the output of amplifier85 corresponds to the first term gKP on the right side of equation 15-2.The output of amplifier 88 corresponds to the second term on the rightside of equation l5-2. The output of adder 84 corresponds to the rightside of equation [5-2.

As is apparent from the theory described hereinbefore, all factors inthe kinematic system of the vehicle and wheel being braked are reflectedin the set wheel velocity w,. The coefficient of friction of the roadsurface is also taken into consideration. Therefore, the actual wheelvelocity w may be controlled in comparison with the set wheel velocityw,

FIG. 7 illustrates another embodiment of the control circuit 8 in thesystem of FIG. 1. Here the control circuit is simplified to improve thestability of the control system. In FIG. 6 the wheel deceleration wdepends upon the rate of pressure change or pressure speed P of thehydraulic pressure P. Thus, the pressure speed P is taken intoconsideration. As can be seen from FIG. 4 the change in pressure islinear. Thus the pressure speed P' or rate of change of the pressure isconstant. Therefore there is no theoretical inconsistency if thepressure speed P is set at a constant value. For this reason the controlcircuit 8 of FIG. 7 eliminates the differentiator 86 and the multiplier87 from its circuit. Here the n-factor of the linear amplifier 88 is setin accordance with the constant pressure speed P of the pressuremodulator 9.

In FIG. 7 the function of adder 84, subtractor 82,

memory 81, and integrator 83 are combined in a capacitor 81b and a diode81a, as well as the connection between the two, in a memory circuit 81'.The voltage proportional to the wheel velocity w, asdetected by thewheel velocity detector 7, is applied to one pole of a comparator 89'.At the same time the voltage proportional to the velocity w is appliedto the initial velocity memory circuit 81'. The pressure detector 6applies a voltage proportional to the hydraulic pressure P to the baseof a transistor 85a. The latter forms a linear amplifier 85' with aresistor 85b. The current Ia corresponding to the first term a on theright side of equation 15-2 is passed to the collector of the transistor85 The current 16 corresponding to the rate of change P of pressure Pand maintained at a constant value and proportional to the value ofvelocity v is passed to a resistor 88.

In other words, the potential corresponding to the initial velocity wcharged to the capacitor 81b is decreased by the currents Ia and Iscorresponding to a and s respectively, thereby to obtain the set wheelvelocity w, 1

The set wheel velocity w, is applied to the second terminal of thecomparator 89' in the reverse polarity with respect to the first pole.Thus current issues from the comparator 89 only when w is lower than w,and the electromagnetic valve coil of the pressure modulator is excitedto decrease the hydraulic pressure.

According to this embodiment of the invention the brake, or braking,pressure speed P is entered as a constant value. By virtue of thisembodiment the circuit for obtaining the differential of the pressure Pis eliminated. Of course, it is possible to make the braking torque T'constant as in equation 15-3 instead of the brake pressure speed P.

FIG. 8 illustrates still another, simpler, embodiment of the invention.FIG. 8 differs from FIG. 7 in that the base of transistor a is biased bya fixedvoltage 6. This voltage represents the braking pressure P. Therationale for the structure of FIG. 8 is as follows:

The wheel deceleration w can be controlled at a constant value if acertain predetermined corrolation is provided between the brakingpressure P and the rate at which the brake pressure changes P', and thewheel deceleration w is determined on the basis of the vehicle velocityv. Under these circumstances thebraking pressure detector 6 as well asthe differentiator for obtaining the pressure applications P are nolonger necessary.

If the vehicle velocity v is assumed to be constant in equation 15-2 thewheel deceleration w derived by that equation is expressed as the sum ofa term a proportional to the braking pressure P and the term eproportional to the pressure speed or pressure application speed P.Consequently, if the characteristics of the system, namely thecharacteristics that regulate the pressure, are such as to make a econstant, the deceleration w can always be set at a constant value nomatter how the slip ratio changes. However, the deceleration w varieswith the vehicle velocity. Consequently, in constructing the circuit ofthe skid control system so as to ensure substantially optimum skidcontrol, it is necessary to provide a compensating circuit adapted toincrease w' when v is high and to decrease w' when v is low.

Assuming w and v, to be constant a relationship may be obtained betweenthe braking pressure P and the pressure applications P from the equation15-2. Thus gKP Ktan Pv w C constant This can be rewritten as follows:

C,P C C Solving this differential equation;

' c m c,P c l c Arranging the above equation with respect to P and t, weobtain;

P= [C t/C t C C where C C,, C, and C are all constant. 180

In other words, for equation 16 to prevail the pressure modulator 9should exhibit the characteristic in which the hydraulic pressure P andthe time tsatisfy the equations 17. All constants C C,, C,, and C arecharacteristic values which can be obtained from the vehicle beingbraked.

In FIG. 8 the voltage proportional to the wheel velocity w is applied toone input terminal of a comparator 89' and to the diode 81a of theinitial velocity memory circuit 81. The latter circuit, in FIG. 8consists of the diode 81a and the capacitor 81b. According to thisembodiment of the invention the braking pressure detector is no longerrequired. The voltage source 6' at the base of transistor 85acorresponds to the constant C, in equation 16. The potential biases thebase of the transistor 85a which forms a linear amplifier 85' with theresistor 85b.

Current corresponding to the constant C passes through the collector oftransistor 850'. Since the deceleration w varies with the change in thevehicle velocity v, the resistor 88' is connected to compensate forchanges due to vehicle velocity v. Thus the potential corresponding tothe set wheel velocity w, obtained from the wheel deceleration w isapplied to the second input terminal of the comparator 89'.

FIG. 9 illustrates a control circuit utilizing the principles of thecircuit 8 in FIG. 8. Here the base of a transistor 13 receives theoutput voltage V from the wheel velocity detector 7. The transistor 13,connected as an emitter follower, produces a voltage Vw proportional tothe wheel velocity w across an emitter resistor 14. A second transistor15 which receives the voltage V from the wheel velocity detector 7 atits base, attempts to charge and discharge an emitter capacitor 17,through its collector resistor 16, to the voltage Vw. The voltage Vwultimately forms the voltage Vt corresponding to the set wheel velocityw, across the capacitor 17.

Connected to the emitter outputs of transistors 13 and 15 are the basesof two transistors 18 and 19. A transistor 20 and an emitter resistor 21are connected in series with the emitters of transistors 18 and 19. Thetransistors 18,19 and 20 and the resistor 21, 21 and 22 form adifferential amplifier 23. Thus the transistor 18 conducts when thevoltage V, stored across the capacitor prevents the voltage at the baseof transistor 18 from following the voltage Vw downwardly. An outputresistor 22 at the collector of transistor 18 forms a voltage drop whenthe voltage Vw and the voltage V, are compared. The transistor 18 mayloosely be said to conduct when the transistor 15 conducts heavily andthe transistor 19 to conduct with the transistor 13.

A transistor 24 which ls rendered conductive by the voltage drop at thecollector of transistor 18 connects to the transistor 22. The transistor24, with its collector resistor 25, generates an output voltage inresponse to the input voltage from the transistor 18 and applies itthrough a diode 26 to the base of a transistor 27. The transistor 27 isconnected through a pair of lines 10 to the pressure modulator 9 so asto transmit a pressure reducing signal.

The capacitor 17 is connected in parallel with a resis tor 29, atransistor 30, and a resistor 31 in a discharge circuit 28 in order toestablish the set wheel velocity w, A constant voltage circuit 34composed of a resistor 32 and a Zener diode establishes a fixed voltageat the base of transistor 20 in the differential amplifier 23. It alsoestablishes the constant potential at the base of the transistor 30 andone side of the resistor 29 in the discharge circuit 28. This constantpotential moreover appears at one terminal of the wheel velocitydetector 7.

In order to prolong pressure reduction the emitter base circuit of atransistor 36 receives the voltage appearing across the resistor 16. Thetransistor 36 forms its output voltage by means of a collector resistor37. This output voltage appears at a switch 38. A contact 380 of theswitch 38 is connected to the transistor 27 as well as to a biasresistor 40 through a diode 39.

Another contact 38b of the switch 38 connects to a resistor 41 and atransistor 42. The transistor 42 is connected to the pressure modulator9 through the lines 11. This signal is applied to the electric lines 11only when the contact 38b is connected to the armature of the switch 38.The circuit of FIG. 9 is actuated electrically by a switch interlockedwith the engine switch, a switch actuated by the brake pedal, or thelike.

The circuit 8 of FIG. 9 actuates the pressure regulator or modulator 9illustrated in FIG. 10. Here a pressure modulating unit 43 reduces thebrake pressure of the wheel cylinder 5. A changeover valve 44 isactuated by means of the pressure reducing signal transmitted throughthe electric lines 10 from the control circuit 8. A retaining valve 45is operated by signals transmitted over electric lines 11. A pressureregulating valve 46 controls the operation of the pressure modulatingunit 43 on the basis of signals received from the control circuit 8 andthe brake pressure.

The pressure modulating unit 43 is composed of a large-diameter cylinderbody 49 having ports 47 and 48 located opposite to each other, and asmall-diameter cylinder body 53 having a narrowed portion 50 as well asports 51 and 52. A diaphragm 54 in the largediameter cylinder body 49divides the interior thereof to form a negative pressure chamber 55having a spring 56 on one side and an operating chamber 57 on the otherside. Projecting from the center of the diaphragm 54 is a piston 60. Thepiston 60 extends through a seal 59 and terminates in a narrow end 58that projects into the small-diameter cylinder body. Within thesmalldiameter cylinder body 53, the narrowed portion 50 and the seal 59form a modulating chamber. At the other side of the narrowed portion 50the body 53 forms an introduction chamber 62 wherein a spring 63 pushesa check ball 64 against the opening formed by the narrowed portion 50.

In the changeover valve 44 a valve body 69 travels along a cylinder body68 having a port 65 and two other ports 66 and 67 which are changedover. When the control circuit issues a pressure reducing signal throughthe wires 10, the electromagnetic coil 70 excites the valve body 69.This moves the valve body to its uppermost position where it blocks theport 66 and brings the port 65 into communication with the port 67. Whenno signal is transmitted and the valve body 69 is deenergized, thelatter travels into its lower position and the port 65 communicates withthe port 66.

In the retaining valve 45 a valve body 75 slides within a cylinder body74 having ports 72 and 73 located at opposite sides thereof. When thecontrol circuit 8 issues a signal to the wires 11 the electromagneticcoil 71 moves the valve body 75 into its uppermost position. This closesthe port 72.

In the pressure speed regulating valve 46 a throttle valve 81 slideswithin a body 80 having ports 77, 78 and 79 on three sides thereof. Aspring biases the valve 81 in one direction.

Hydraulic lines connect the port 51 of the pressure modulating unit 43to the master cylinder 2, and the port 52 of the unit 53 to the wheelcylinder as well as to the port 77 of the pressure speed regulatingvalve. The port 48 of the pressure regulating unit 43 is connected to anegative pressure source 82 and the port 66 of the changeover valve 44.The port 67 of the changeover valve 44 opens to the atmosphere. The port65 connects to the port 47 of the pressure modulating unit through twoports 72 and 73 of the retaining valve 46 and two ports 78 and 79 of thepressure speed regulating valve.

The operation of FIGS. 1, 9 and can best be understood by referring toFIGS. 11a, 11b and 11c. When a vehicle travels normally such as duringthe times from t to t, in FIGS. 11a, 11b and He the wheel velocity isequal to the vehicle velocity and almost constant. At

this time the capacitor 17 of the differential amplifier ulator 9 isdeenergized. The port 65 then communicates with the port 66. Because theretaining valve 45 is not operated the port 72 communicates with theport -73. Since no braking pressure exists in the pressure speedregulating valve 46 the valve body 81 is retracted or biased by thespring 76 to the rearmost position so as to open port 79. Therefore, thechambers 55 and 57 located on opposite sides of the diagragm 54 in thepressure modulating unit 43 exhibit the same negative pressure. Thespring 56 thus pushes the diaphragm 54 to the right. The end portion 58of the piston 60 moves the check ball 64 to the right against thepressure of the spring 63. This brings the introduction chamber 62 intocommunication with the modulating chamber 61. Thus, the master cylinder2 communicates with the wheel cylinder 5 to perform the normal brakingoperation.

When the emergency brake is applied at time t while traveling under theabove described conditions and the braking pressure is increasedlinearly as shown in FIG. 110 to decelerate the wheel velocity, thevoltage V, across the capacitor 17 and the control circuit 8 isdischarged by the transistor 30 and the resistor 29 of the dischargecircuit 28. The rate of discharge is in accordance with the decrease inthe voltage V,, representing the wheel velocity. This causes a decreasein voltage across the capacitor. However, during the initial brakingperiod from time t, to times t the wheel deceleration is comparativelysmall. It is smaller than the drop rate due to the discharge of thevoltage Vt on capacitor 17. Thus, both voltages Vw and Vt drop to anequal value. The transistors l5, 18, 24 and 27 then remainnon-conductive and no pressure reducing signal is issued. Consequently,the pressure regulator or modulator 9 remains in the same condition asit was during the normal movement of the vehicle. At the time t thecoefficient of friction between the wheel and the road surfaceapproaches a maximum. The slip ratio is suddenly increased and the wheelvelocity decreases rapidly. In this case the wheel deceleration suddenlyincreases as shown in FIG. llb. In the control circuit 8 the voltagedrop rate of the voltage Vw due to the wheel deceleration becomes largerthan the voltage drop rate of voltage Vt due to the discharge of the setdeceleration. Thus the transistor 15 becomes completely nonconductive.The voltage Vt at the base of transistor 18 now exceeds the voltage Vwat the base of the transistor 19. The transistors 18, 24 and 27 conduct.This generates an output voltage. The voltage is applied as a pressurereducing signal to the electromagnetic coil of the changeover valve 44of the pressure modulator 9.

In the pressure modulator 9 of the electromagnetic coil 70 of thechangeover valve 44 moves the valve body 69 to bring the port 67 intocommunication with the port 65. Thus the operating chamber 57 of thepressure modulating unit 43 is exposed to atmospheric pressure. Thismoves the diaphragm 54 to the left against the force of the spring 56.The diaphragm 54 carries the piston 60 to the left. The spring 63 nowpresses the check ball 64 to close the opening at the narrowed portion50. This interrupts communication between the chambers 61 and 62. Thehydraulic pressure line 6 between the master cylinder 2 and the wheelcylinder 5 is thus interrupted. As a result of the above the volume ofthe modulating chamber 61 is increased due to the movement of the piston60 to the left. The

braking pressure of the wheel cylinder is decreased because of reducedpressure and its own characteristic, as shown in FIG. 110.

At this time the valve body 81 of the pressure speed regulating valve 46is moved by the braking pressure applied to the port 77 to change theopening area of the port 79 and regulate the flow rate of atmosphericpressure by throttling. When the braking pressure is low at the initialperiod of braking the braking pressure changing speed is increased byincreasing the flow of atmospheric pressure and consequently the volumeof the modulating chamber 61 of the pressure modulating unit 43. As thebraking pressure is increased the braking pressure changing speed isdecreased by decreasing the flow of atmospheric pressure andconsequently the volume of the modulating chamber 61.

As described above, skid control is performed at the time 2,. The wheelvelocity is increased again to approach the vehicle velocity.Consequently the voltage Vw corresponding to the wheel velocity isincreased. At the time 1 the voltage exceeds the voltage Vt developed bythe capacitor 17 so as to correspond to the set deceleration. Thus, thetransistors 18, 24 and 27 of the control circuit 8 are renderednon-conductive at the time t,. This eliminates the pressure reducingsignal being passed to the pressure modulator 9. At the same time thetransistor is rendered conductive to charge the capacitor 17.Consequently, the electromagnetic coil 70 of the changeover valve 44 inthe pressure modulator is deenergized and the valve body 69 moved tobring the port 66 into communication with the port 65. Thus negativepressure is introduced into the operating chamber 57 of the pressuremodulating unit 43 and the piston 60 is moved to the right by means ofthe spring 56.

At this time the braking pressure is applied to the port 77 of thepressure speed regulating valve to move the valve body 81 forward, andthereby to throttle the port 79. Consequently the negative pressure inthe operating chamber of the pressure modulating unit 43 is low, andtherefore the movement of the piston is not large enough to project thecheck ball 64 to establish communication between the chambers 61 and 62.Thus the volume of the chamber 61 is decreased. Therefore the brakingpressure of the wheel cylinder 5 is increased in accordance with thedecrease in the volume. This is shown in FIG. 11c. It performs the sameoperation as is the case when the pressure application signal isapplied.

The wheel velocity being restored to perform braking at the time 1,reaches a maximum at the time t and then decreases again. From the timet, on the voltage Vw corresponding to the wheel velocity becomes equalto the voltage Vt corresponding to the set velocity in the same manneras they were during the period from r, to r,. At the time t, thecoefficient of friction approaches a maximum as it did at the times t,and the pressure reducing signal issues from the control circuit 8 andthe wheel deceleration is suddenly decreased as shown in FIG. 11b. Thusskid control is performed by means of the pressure modulator 9.

The above described operations are continuously repeated several timesfrom the time t, on so as to perform optimum braking.

In the above described braking process the switch 38 in the controlcircuit 8 may be placed against the contact 38a to cause the transistor36 to conduct during the periods of time from to t and from to I, whenthe wheel velocity is being increased and when the capacitor 17 is beingcharged. Then, even if the transistor 24 is rendered non-conductivesignals through the diode 39 render the transistor 27 conductive. Thelatter then continues to apply pressure reducing signals to the pressuremodulator 9. Thus the pressure reducing time is prolonged as shown bythe broken line in FIG. 110. This further accelerates the recovery ofthe wheel velocity.

In order to obtain the same effect as described above, the switch 38 ofthe control circuit 8 is switched to close against the contact 38b. Thisrenders the transistor 42 conductive during the same time intervals asdescribed above. This causes issuance of pressure reducing signalsthrough the lines 11 to the pressure modulator 9. Consequently theelectromagnetic coil 71 of the retaining valve 45 in the pressuremodulator is excited and the port 72 closed by the movement of the valvebody 75. Thus the atmospheric pressure is supplied to theoperatingchamber 57 of the pressure modulating unit 43 during the timeperiod of to 1,. The pressure of the braking fluid is maintainedconstant during this period of time as shown by the alternate long andshort line in FIG. 11c.

According to another embodiment of the invention the system of FIGS. 9and 10 are modified to include the inputs illustrated in FIGS. 6 and 7.

As described so far, according to this invention, the wheel decelerationis established from the vehicle deceleration, the vehicle velocity, therate at which the braking fluid pressure is changed in the gradient ofthe characteristic curve shown in the relationship between thecoefficient of friction and the road surface and the wheel slip ratio.Skid control is performed by comparing the set wheel velocity obtainedin accordance with the set deceleration and the actual wheel velocity.Consequently, compared with systems in which a chosen value isarbitrarily adopted as the set deceleration, the skid control systemembodying features of this invention performs skid control optimally inaccordance with the changes and the kind of road surface, vehiclevelocity, and slip ratio.

Skid control systems embodying features of this invention may include amechanical, hydraulic, or pneumatic arrangement instead of theelectronic circuit employed in the above-described embodiment. Where amechanical element is employed, for example, the capacitor 17 of thecontrol circuit 8 may be replaced with a flywheel. The dischargingresistor 30 may be replaced with a friction brake adapted to deceleratethe flywheel. The charging resistor 15 would then be replaced by aone-way clutch adapted to accelerate the flywheel. The differentialamplifier would be composed of a governor mechanism etc.

It should be noted that in FIG. 6 the memory 81 can be composed of acapacitor being charged through a diode. The subtractor circuit 82 maybe composed of an inverter and an adder.

In FIG. 9 the combination of the transistor 30 with its resistor 31 andthe resistor 29 operate similar to the transistor 85a, the resistor 85band the resistor 88. In effect the transistor 15 charges the capacitor17 to a voltage Vt corresponding to the voltage Vw. At the same time thetransistor 30 and its resistor 31 discharge the capacitor 17 at aconstant rate. Simultaneously the resistor 29 discharges the capacitor17 along the normal exponential discharge path. The combined dischargerate is the sum of the linear and exponential rates. As long as thevelocity is constant these rates correspond to a value proportional tothe brake fluid pressure and a value proportional to the rate of changeof the pressure. As long as the velocity is constant the transistor 15keeps recharging the capacitor 17 despite the discharging effect of theparallel circuit composed of transistor 30 with its resistor 31 and theresistor 29.

The circuit 28 discharges the capacitor at the above rate. As long thevoltage applied to the bases of transistors l and 13 declines at aslower rate the transistor 15 will tend to keep charging the capacitor17 so that the voltage at the base of transistor 18 follows the voltageat the base of the transistor 19. However, where the voltage V at theoutput of the detector 7 declines at a rate so that the voltage at thebases of transistors 18 and 19 try to go down faster than the dischargerate of the circuit 28, the capacitor 17 will not follow and will forcethe base of the transistor 18 to remain higher than the base of thetransistor 19. This renders transistors 18, 24 and 27 conductive.

In FIG. it should be noted that the negative feedback produced by theconnection from the port 52 to the port 77, and the operation of thevalve 46 constrains the entire system to operate according to equation17. In this way the skid control system of FIGS. 19 and 10 operate onthe basis of equation 16 and equation 152.

As is apparent form the equations 1 to -3 all factors in the kinematicsystem of the vehicle and wheel being braked are reflected in the setwheel velocity w,. The coefficient offriction of a road surface is alsotaken into consideration. Therefore, the actual wheel velocity w iscontrolled in comparison with the set wheel velocity w,.

The invention has three aspects. According to the first aspect of theinvention the control of the wheel deceleration is performed accordingto the equations l5-l, l5-2 and 15-3. Therefore, the signalcorresponding to the vehicle deceleration, which may be expressed by thebraking pressure or braking torque, and the signal corresponding to theproduct of the gradient tan0 of the u-acurve, braking pressure speed P(or torque changing speed T) and the vehicle velocity are produced. Theset deceleration of a wheel expressed by the sum of both signals isobtained. Thus skid control is performed by the comparison of the thusobtained set wheel deceleration and the actually detected wheeldeceleration.

According to another aspect of the invention, the braking pressure speedI" is selected as a constant value. By virtue of this construction acircuit for obtaining the braking pressure speed P can be eliminated. Ofcourse it is possible to make the braking torque T, constant instead ofthe braking pressure speed P.

According to still another aspect of this invention, a specificpredetermined corrolation is provided between the braking pressure P andthe braking pressure speed P. Thus the wheel deceleration to becalculated by taking into consideration the signal corresponding to thevehicle velocity can be made substantially constant for variousconditions of road surface. In this case the detection of the brakingpressure is no longer required, because a predetermined corrolation isproduced between P and P. This greatly simplifies construction of theapparatus.

III

While embodiments of the invention have been described in detail it willbe obvious to those skilled in the art that the invention may beembodied otherwise without departing from its spirit and scope.

What is claimed is:

1. An apparatus for determining whether the force supplied by the brakesof a vehicle to its wheels is too high, comprising detecting means fordetecting the velocity of the wheel, memory means responsive to saiddetecting means for establishing a value corresponding to the velocityof the wheel, sensing means coupled to said memory means for exhibitinga value dependent upon the value in said memory means, control meanscapable of changing the value exhibited by said sensing means linearlyand exponentially for modifying the value exhibited by said sensingmeans linearly and exponentially, said control means including first andsecond portions respectively modifying the exhibited value linearly andexponentially, and comparator means coupled to said sensing means andsaid detecting means-for comparing the value exhibited at said sensingmeans with the value of said detecting means for producing an outputsignal when the value of said sensing means exceeds a predeterminedrelationship between the values of said sensing means and said detectingmeans.

2. An apparatus as in claim 1, wherein said portions are connected inparallel to each other.

3. An apparatus for determining whether the force applied by the brakesof a vehicle to its wheels is too high, comprising memory means forestablishing a value corresponding to the velocity of the wheel, firstcontrol means capable of changing the value in said memory meanslinearly, second control means capable of changing the value in saidmemory means exponentially, adding means for connecting said first andsecond control means to said memory means so as to change the value insaid memory means on the basis of the sum of the linear and exponentialchange, and comparator means connected to said adding means forcomparing the value in said memory means with an input valuecorresponding to the velocity of the wheel and for producing an outputsignal when the value in said memory means exceeds the input valuecorresponding to the velocity of the wheel.

4. An apparatus as in claim 3, wherein said memory means includes energystorage means.

5. An apparatus as in claim 3, wherein said memory means includescapacitor means and unidirectional means for applying a voltagecorresponding to the wheel velocity across said capacitor means.

6. An apparatus as in claim 5, wherein said first control means includeslinear amplifying means for forming a path of constant current flow.

7. An apparatus as in'claim 5, wherein said second control meansincludes a resistor.

8. An apparatus as in claim 5, wherein said adding means includes acircuitconnecting each of said control means in parallel across saidcapacitor means.

9. An apparatus as in claim 8, wherein said first control means includeslinear amplifying means for forming a path of constant current flow.

10. An apparatus as in claim 9, wherein said second control meansincludes a resistor.

11. An apparatus as in claim 10, wherein said first control meansincludes linear amplifying means for forming a path of constant currentflow.

12. An apparatus as in claim ll, wherein said comparator means includesa differential amplifier.

[3. An apparatus as in claim 12, further comprising pressure modulatingmeans for modulating the braking force applied to the wheel.

14. A skid control system for a vehicle having a wheel and brakes forapplying a braking force to the wheel, comprising a wheel velocitydetector for detecing'the velocity of the wheel, an initial velocitymemory circuit for memorizing the wheel velocity when a braking force isapplied to the wheel, first detector means for obtaining an outputcorresponding to the vehicle deceleration, second detector means forobtaining an output corresponding to the braking force applied to thewheel, differentiator means coupled to said second detector means todifferentiate the output of said second detector means, multiplier meansconnected to said differentiator means for producing an outputproportional to the product of the output of said differentiator meansand the velocity of the vehicle and the product of the gradient of thecharacteristic curve determined by the coefficient of friction between aroad surface and a wheel and a wheel slip ratio in the range of slipratios less than that at which the characteristic curve is curved, addermeans coupled to said first detector means and said multiplier means foradding the outputs of said first detector means and said multipliermeans to obtain a value corresponding to a safe wheel deceleration,integrator means coupled to said adder means for integrating the valuecorresponding to the safe deceleration, subtractor means coupled to saidmemory means and said integrator means for subtracting the timeintegration of the value corresponding to the safe deceleration from theoutput of said'wheel velocity detector, comparator means coupled to saidvelocity detector and said subtracting means for producing a pressurereducing signal when the output of said subtracting means exceeds theoutput of said detector, and pressure modulator means responsive to saidcomparator means for regulating the braking force in accordance with anoutput signal from said comparator means.

15. A skid control system as in claim 14, wherein said multiplier meansresponds to the output of said subtracting means for responding to avalue corresponding to the vehicle velocity. v

16. A skid control system for a vehicle having a wheel and a brake forapplying a braking force to the wheel, comprising a wheel velocitydetector meansfor detecting the wheel velocity, initial velocity memorycircuit means for memorizing the wheel velocity at the initiation ofbraking, braking force detector means for producing an outputproportional to the vehicle deceleration, braking force speed means forproducing an output corresponding to the rate of change of the brakingforce, multiplier means coupled to said braking force speed means forproducing a signal'corresponding to the product of the vehicle velocityand the output of said braking force speed means as well as the gradientof the characteristic curve determined by the coefficient of frictionbetween a road surface and a wheel and the wheel slip ratio in the rangeof slip ratios less than that at which said characteristic curve iscurved, adder means coupled to said multiplier means for adding bothoutputs of said braking force detecotr means and said multiplier meansfor obtaining dwalue corresponding to a set deceleration, integratormeans coupled to said adder means for producing a value corresponding tothe integral of the set wheel acceleration, subtractor means connectedto said memory circuit means and said integrator means for producing asignal corresponding to the difference between the output of said memorymeans and the output of said integrator means, comparator means coupledto said subtractor means and said detector means for producing a brakingforce reducing signal when the output of said subtractor means exceedsthe output of said detector means, and force modulator means coupled tosaid comparator means for regulating the braking force with a constantforce application rate of change in accordance with the output signal ofsaid comparator means.

17. A system as in claim 16, wherein the output of said subtractor meansis coupled to said multiplier means.

18.'A skid control system for a vehicle having a brake arrangement forapplying abraking pressure to a wheel of the vehicle, comprising wheelvelocity detector means for detecting the velocity of the wheel, initialvelocity memory means for memorizing the wheel velocity at the time ofthe start of a braking action,subtractor means responsive to said memorymeans for obtaining a set wheel velocity by s'ubstracting a timeintegration of a set deceleration from an initial velocity, brakingpressure sensing means for detecting the braking pressure, linearamplifier means coupled to the output of said subtractor means and tosaid sensing means for amplifying the set wheel velocity to obtain anoutput substantially corresponding to the product of the vehiclevelocityand the rate of change of the braking pressure as well as thegradient of the characteristic curve determined by the coefficient offriction between a road surface and a wheel and the wheel slip ratio inthe range of slip ratios less than that at which the characteristiccurve is curved, comparator means for comparing the wheel velocity andthe set wheel velocity for issuing a braking pressure reducing signalwhen the wheel velocity is less than the set wheel velocity, andpressure modulator means for reducing the braking pressure in accordancewith said signal by providing the characteristic to the pressuremodulating speed so that the sum of the value. representing the brakingpressure and the value representing the change in braking pressurebecome constant. g

19. A skid control system for varying the braking pressure applied by abrake to the wheel of a vehicle, comprising velocity measuring means formeasuring the velocity of the wheel, storage means for storing a valuecorresponding to the output of said measuring means, first control meanscapable of changing the level of the value in said storage meanslinearly, second control means capable of changing the level of thevalue in said storage means exponentially, adding means for connectingsaid first and second control means to said storage means so as tochange the value in said storage means on the basis of the sum of thelinear and exponential change, comparator means responsive to saidadding means and said measuring means for comparing the value in saidadding means and said measuring means and producing an output signalwhen the value in said storage means exceeds the value in said measuringmeans, and braking force modulating means responsive to said comparatormeans for regulating the braking force applied by the brake to thewheel.

20. A system as in claim 19 wherein said braking force modulating meansincludes a negative feedback system for delaying the effect saidmodulating means has upon the braking force in response to saidcomparator means.

21. A system as in claim 20 wherein said braking force modulating meanshas a characteristic obeying the expression (C t/qt C C;,, where trepresents time and C C C and C are constants.

22. A system as in claim 20 wherein said first control means includeslinear aplifying means for forming a path of constant current flow andwherein said second control means includes a resistor.

23. A system as in claim 22 wherein said braking force modulating meansincludes a pressure control system, said pressure control system havingan output, said pressure control system having an input, said pressurecontrol system having a throttling valve responsive to said output andforming a feedback in said system.

24. A system as in claim 19 wherein said storage means includescapacitor means and unidirectional means for applying a voltagecorresponding to the wheel velocity across said capacitor means.

25. A system as in claim 24 wherein said first control means includeslinear amplifying means for forming a path of constant current flow.

26. A system as in claim 24 wherein said second control means includes aresistor.

27. A system as in claim 24 wherein said adding means includes a circuitconnecting each of said control means in parallel across said capacitormeans.

28. A system as in claim 27 wherein said first control means includeslinear amplifying means for forming a path of constant current flow andwherein said second control means includes a resistor.

29. A system as in claim 19, wherein said control means include meansfor prolonging the modulaton of said braking force when the value insaid storage means no longer exceeds the value in said measuring means.=1 =l=

1. An apparatus for determining whether the force supplied by the brakesof a vehicle to its wheels is too high, comprising detecting means fordetecting the velocity of the wheel, memory means responsive to saiddetecting means for establishing a value corresponding to the velocityof the wheel, sensing means coupled to said memory means for exhibitinga value dependent upon the value in said memory means, control meanscapable of changing the value exhibited by said sensing means linearlyand exponentially for modifying the value exhibited by said sensingmeans linearly and exponentially, said control means including first andsecond portions respectively modifying the exhibited value linearly andexponentially, and comparator means coupled to said sensing means andsaid detecting means for comparing the value exhibited at said sensingmeans with the value of said detecting means for producing an outputsignal when the value of said sensing means exceeds a predeterminedrelationship between the values of said sensing means and said detectingmeans.
 2. An apparatus as in claim 1, wherein said portions areconnected in parallel to each other.
 3. An apparatus for determiningwhether the force applied by the brakes of a vehicle to its wheels istoo high, comprising memory means for establishing a value correspondingto the velocity of the wheel, first control means capable of changingthe value in said memory means linearly, second control means capable ofchanging the value in said memory means exponentially, adding means forconnecting said first and second control means to said memory means soas to change the value in said memory means on the basis of the sum ofthe linear and exponential change, and comparator means connected tosaid adding means for comparing the value in said memory means with aninput value corresponding to the velocity of the wheel and for producingan output signal when the value in said memory means exceeds the inputvalue corresponding to the velocity of the wheel.
 4. An apparatus as inclaim 3, wherein said memory means includes energy storage means.
 5. Anapparatus as in claim 3, wherein said memory means includes capacitormeans and unidirectional means for applying a voltage corresponding tothe wheel velocity across said capacitor means.
 6. An apparatus as inclaim 5, wherein said first control means includes linear amplifyingmeans for forming a path of constant current flow.
 7. An apparatus as inclaim 5, wherein said second control means includes a resistor.
 8. Anapparatus as in claim 5, wherein said adding means includes a circuitconnecting each of said control means in parallel across said capacitormeans.
 9. An apparatus as in claim 8, wherein said first control meansincludes linear amplifying means for forming a path of constant currentflow.
 10. An apparatus as in claim 9, wherein said second control meansincludes a resistor.
 11. An apparatus as in claim 10, wherein said firstcontrol means includes linear amplifying means for forming a path ofconstant current flow.
 12. An apparatus as in claim 11, wherein saidcomparator means includes a differential amplifier.
 13. An apparatus asin claim 12, further comprising pressure modulating means for modulatingthe braking force applied to the wheel.
 14. A skid control system for avehicle having a wheel and brakes for applying a braking force to thewheel, comprising a wheel velocity detector for detecing the velocity ofthe wheel, an initial velocity memory circuit for memorizing the wheelvelocity when a braking force is applied to the wheel, first detectormeans for obtaining an output corresponding to the vehicle deceleration,second detector means for obtaining an output corresponding to thebraking force applied to the wheel, differentiator means coupled to saidsecond detector means to differentiate the output of said seconddetector means, multiplier means connected to said differentiator meansfor producing an output proportional to the product of the output ofsaid differentiator means and the velocity of the vehicle and theproduct of the gradient of the characteristic curve determined by thecoefficient of friction between a road surface and a wheel and a wheelslip ratio in the range of slip ratios less than that at which thecharacteristic curve is curved, adder means coupled to said firstdetector means and said multiplier means for adding the outputs of saidfirst detector means and said multiplier means to obtain a valuecorresponding to a safe wheel deceleration, integrator means coupled tosaid adder means for integrating the value corresponding to the safedeceleration, subtractor means coupled to said memory means and saidintegrator means for subtracting the time integration of the valuecorresponding to the safe deceleration from the output of said wheelvelocity detector, comparator means coupled to said velocity detectorand said subtracting means for producing a pressure reducing signal whenthe output of said subtracting means exceeds the output of saiddetector, and pressure modulator means responsive to said comparatormeans for regulating the braking force in accordance with an outputsignal from said comparator means.
 15. A skid control system as in claim14, wherein said multiplier means responds to the output of saidsubtracting means for responding to a value corresponding to the vehiclevelocity.
 16. A skid control system for a vehicle having a wheel and abrake for applying a braking force to the wheel, comprising a wheelvelocity detector means for detecting the wheel velocity, initialvelocity memory circuit means for memorizing the wheel velocity at theinitiation of braking, braking force detector means for producing anoutput proportional to the vehicle deceleration, braking force speedmeans for producing an output corresponding to the rate of change of thebraking force, multiplier means coupled to said braking force speedmeans for producing a signal corresponding to the product of the vehiclevelocity and the output of said braking force speed means as well as thegradient of the characteristic curve determined by the coefficient offriction between a road surface and a wheel and the wheel slip ratio inthe range of slip ratios less than that at which said characteristiccurve is curved, adder means coupled to said multiplier means for addingboth outputs of said braking force detecotr means and said multipliermeans for obtaining a value corresponding to a set deceleration,integrator means coupled to said adder means for producing a valuecorresponding to the integral of the set wheel acceleration, subtractormeans connected to said memory circuit means and said integrator meansfor producing a signal corresponding to the difference between theoutput of said memory means and the output of said integrator means,comparator means coupled to said subtractor means and said detectormeans for producing a braking force reducing signal when the output ofsaid subtractor means exceeds the output of said detector means, andforce modulator means coupled to said comparator means for regulatingthe braking force with a constant force application rate of change inaccordance with the output signal of said comparator means.
 17. A systemas in claim 16, wherein the output of said subtractor means is coupledto said multiplier means.
 18. A skid control system for a vehicle havinga brake arrangement for applying a braking pressure to a wheel of thevehicle, comprising wheel velocity detector means for detecting thevelocity of the wheel, initial velocity memory means for memorizing thewheel velocity at the time of the start of a braking action, subtractormeans responsive to said memory means for obtaining a set wheel velocityby substracting a time integration of a set deceleration from an initialvelocity, braking pressure sensing means for detecting the brakingpressure, linear amplifier means coupled to the output of saidsubtractor means and to said sensing means for amplifying the set wheelvelocity to obtain an output substantially corresponding to the productof the vehicle velocity and the rate of change of the braking pressureas well as the gradient of the characteristic curve determined by thecoefficient of friction between a road surface and a wheel and the wheelslip ratio in the range of slip ratios less than that at which thecharacteristic curve is curved, comparator means for comparing the wheelvelocity and the set wheel velocity for issuing a braking pressurereducing signal when the wheel velocity is less than the set wheelvelocity, and pressure modulator means for reducing the braking pressurein accordance with said signal by providing the characteristic to thepressure modulating speed so that the sum of the value representing thebraking pressure and the value representing the change in brakingpressure become constant.
 19. A skid control system for varying thebraking pressure applied by a brake to the wheel of a vehicle,comprising velocity measuring means for measuring the velocity of thewheel, storage means for storing a value corresponding to the output ofsaid measuring means, first control means capable of changing the levelof the value in said storage means linearly, second control meanscapable of changing the level of the value in said storage meansexponentially, adding means for connecting said first and second controlmeans to said storage means so as to change the value in said storagemeans on the basis of the sum of the linear and exponential change,comparator means responsive to said adding means and said measuringmeans for comparing the value in said adding means and said measuringmeans and producing an output signal when the value in said storagemeans exceeds the value in said measuring means, and braking forcemodulating means responsive to said comparator means for regulating thebraking force applied by the brake to the wheel.
 20. A system as inclaim 19 wherein said braking force modulating means includes a negativefeedback system for delaying the effect said modulating means has uponthe braking force in response to said comparator means.
 21. A system asin claim 20 wherein said braking force modulating means has acharacteristic obeying the expression (C0t/c1t + C2) + C3, where trepresents time and C0, C1, C2 and C3 are constants.
 22. A system as inclaim 20 wherein said first control means includes linear aplifyingmeans for forming a path of constant current flow and wherein saidsecond control means includes a resistor.
 23. A system as in claim 22wherein said braking force modulating means includes a pressure controlsystem, said pressure control system having an output, said pressurecontrol system having an input, said pressure control system having athrottling valve responsive to said output and forming a feedback insaid system.
 24. A system as in claim 19 wherein said storage meansincludes capacitor means and unidirectional means for applying a voltagecorresponding to the wheel velocity across said capacitor means.
 25. Asystem as in claim 24 wherein said first control means includes linearamplifying means for Forming a path of constant current flow.
 26. Asystem as in claim 24 wherein said second control means includes aresistor.
 27. A system as in claim 24 wherein said adding means includesa circuit connecting each of said control means in parallel across saidcapacitor means.
 28. A system as in claim 27 wherein said first controlmeans includes linear amplifying means for forming a path of constantcurrent flow and wherein said second control means includes a resistor.29. A system as in claim 19, wherein said control means include meansfor prolonging the modulaton of said braking force when the value insaid storage means no longer exceeds the value in said measuring means.